%I
%S 5,11,29,367,149,631,127,1949,541,907,3251,1693,2503,10427,5779,10831,
%T 10007,22229,30631,25301,121123,76207,93047,157627,212557,35729,
%U 119027,1121509,190979,672439,693943,1004027,259099,1646101,675713,1207841
%N a(n)=nextprime[A090116(n)], the smallest prime following squares listed in A090116 and also the distance of a(n) from the preceding prime is 2n.
%F a(n) = nextprime[A090116(n)^2] = nextprime[A090117(n)] = p[1+pi[A090117(n)]] = A007918[A090116[n]].
%e n=7: a(7)=127 because 127113=14=2.7 and 121=11 is between {127,113} closest primes to 121 a suitable square number. Also 127 is the smallest prime with this property.
%t pre[x_ := Prime[PrimePi[x]] nex[x_ := Prime[PrimePi[x]+1] de[x_ := Prime[PrimePi[x]+1]Prime[PrimePi[x]] t=Table[de[w^2], {w, 1, 50000}]; mt=Table[Min[Flatten[Position[t, 2*j]]], {j, 1, 100}] Table[nex[Part[mt, j]^2], {j, 1, Length[mt]}]
%Y Cf. A090116A090118, A007917, A007918, A000720, A000040, A053001, A007491, A000290.
%K nonn
%O 1,1
%A _Labos Elemer_, Jan 09 2004
